Do you think he can see us … African Queen. Photograph: ITV Global Entertainment

Anjelica Huston is recalling her father's reputation for putting his actors through hell on shoots. "Basically," she says, "the one thing you had to do was take it well. My father admired anyone who actually survived it all. Usually, it was a test to see if you had: a) any bravery; or b) a sense of humour. Somehow, if you came out with either of those intact, you graduated."

Anjelica knows all about her father's approach, having acted in four of his films, but on this occasion she's talking about The African Queen, one of John Huston's best loved and most enduring films, which was made in 1951, the year Anjelica was born. The film's status as a classic has now been cemented by a full restoration, involving a frame-by-frame clean-up of the original negatives, which will premiere at Cannes next Wednesday. The making of The African Queen is the stuff of legend: everyone had to "take it well" on this one.

In 1951, Hollywood directors rarely strayed beyond the studio lot, but Huston had already made The Treasure of the Sierra Madre in Mexico, and insisted on shooting The African Queen in Africa – in what was then the Belgian Congo and Uganda. What a surreal congregation it must have been: Humphrey Bogart, Huston's drinking buddy and regular leading man; Bogart's young wife Lauren Bacall, who decided to come along for the ride; Katharine Hepburn, unpopular at the box office and at a crucial stage in her career; and a crew of British technicians, including cinematographer Jack Cardiff and future Bond director Guy Hamilton. Then there was Huston himself: man of action, war veteran and incurable adventurer.

The African Queen is one of those movies that shouldn't work, but does. Set in German east Africa, it's the unlikely story of a starched English missionary (Hepburn) and an unsanitary, gin-swilling boat captain (Bogart), who embark on a self-imposed downriver mission to do their bit in the first world war. If you were pitching it today, you might describe it as Apocalypse Now without the apocalypse, meets Speed without the speed. There are rapids, Germans, breakdowns and hungry leeches to negotiate, but it's less an action thriller than an eccentric opposites-attract romance, fuelled by the unexpected chemistry between its middle-aged leads. "There's a kind of wink behind the movie," says Anjelica. "You feel a kind of complicity – knowing he had these poor actors trapped in the Belgian Congo. I think it adds to the enjoyment."

Angela Allen, one of the few surviving members of the crew, agrees. "It was not an easy shoot," says Allen, who was a 22-year-old continuity checker on the film (she went on to make 13 more movies with Huston). "It certainly wasn't a luxury safari like people go on today. We lived in a camp hacked out of the jungle. You had to leap into bed at night before the mosquitoes could get you, and shake your boots in the morning to make sure there were no centipedes. You washed with red water from the river, and you had a bucket with a string for a shower."

Filming on the river was tricky. The African Queen was too small to shoot in, given the size of the Technicolor cameras, so mock-ups were made of each end of the boat and placed on rafts. The crew would follow behind in more rafts, forming a bizarre flotilla. Bringing up the rear was the sole concession to luxury: Hepburn's private lavatory tent, as stipulated in her contract. "Nobody else was allowed to use it," says Allen.

Hepburn, much like her character, looked on Bogart and Huston's alcoholic regimen with disdain. She made a point of drinking only water, which ironically made her sick. Bogart and Huston, on the other hand, were fine. "All I ate was baked beans, canned asparagus and Scotch whisky," Bogart later recalled. "Whenever a fly bit Huston or me, it dropped dead." The restored print highlights just how green and gaunt Hepburn looked. During some scenes, a bucket was kept off-camera for her to throw up into between takes.

"It was very tough for Katie Hepburn," says Allen. "She had very definite ideas about everything and everybody. One day we were shooting a complicated shot and John said, 'Print it,' and she said, 'You weren't even watching!' John said, 'But I was listening.' 'But you weren't watching,' she insisted and demanded they do it again. To turn the whole flotilla around and come back down the river took hours. John did shoot another take, but we used the original anyway."

There are tales of dysentery, diarrhoea and other tropical ailments, not to mention soldier ants, hippos, black mambas and crocodiles. But adversity drew everyone together. Bogart helped pull the African Queen out of the river when it sank one night, while Bacall mucked in with the catering. She and Hepburn became lifelong friends, and Hepburn ultimately came to admire Huston. Their relationship even became flirtatious, judging by the memoir she wrote later, entitled The Making of the African Queen, or How I Went to Africa With Bogart, Bacall and Huston and Almost Lost My Mind.

When not chronicling her bowel troubles, the book recalls Huston coming to her hut and massaging her when she was sick. It's Bogart she falls for in the film, but The African Queen could be a more accurate reflection of Hepburn's thawing attitude to Huston. With his knowledge of art and literature, his rugged masculinity, and his famously mellifluous voice, the director eventually won her over. "John had such charisma and charm," says Allen. "He could make the ugliest woman in the room feel beautiful. He never got mad, never lost his cool, and the boys would do anything for him. Crews adored him. It was tough, but there were never horrendous rows because John actually steered a very calm ship."

This admiration was mutual, says Anjelica. "I remember, towards the end of his life, we were all having dinner and Dad started to talk about The African Queen. He said, 'Katie was the best female friend I've ever had in my life.' And Lauren Bacall, this little voice at the end of table, piped up, 'Well what about me, John?' And he said, 'Oh honey, you were married to Bogey.'"

Huston had a brutish, chauvinistic side, though. This was recorded by Peter Viertel, a young writer on the shoot who turned his experiences into the novel White Hunter, Black Heart, in which Huston (or rather "John Wilson") is portrayed as a self-indulgent drunk who's more interested in shooting an elephant than a movie. "I always take exception to people who take it too literally," says Anjelica of the book. "I think, for the purposes of novelisation, you have to pump up the volume a bit." Although she admits the gun room in their family home in Ireland had a few stuffed heads, she insists that Huston never shot an elephant.

Still, the story has prevailed. Clint Eastwood turned White Hunter, Black Heart into a movie, in which he both channelled Huston's alpha-male swagger and critiqued it. "He did quite a good job on my dad," says Anjelica, who doesn't remember her father being particularly hands-on. "He was generally away or out of sight. It was a bit of a disjointed family scenario: my father resided in the big house, my mother, brother and I – and our nanny – were in the little house next to it. He always brought a lot of lovely exotic presents back, but, yes, he was largely absent."

John later bonded with Anjelica the only way he knew how: through film. She made her acting debut in 1968 in A Walk With Love and Death, his cumbersome 14th-century romance. "I don't think it's his best movie and it certainly isn't mine," she laughs. "He was tough on me. I had trouble with my lines. It was awful. But he was always hard on actors if he didn't get what he wanted. I just took it personally."

'He directed in an oxygen mask'

Things had improved by the time of Prizzi's Honour in 1985, for which Anjelica received a best supporting actor Oscar. Huston's last film, 1987's The Dead, seemed like a final effort to settle family differences: it was adapted by his son Tony from James Joyce's short story; it starred Anjelica; and it dealt with the regrets of an Irish family. By this stage, Huston was giving way to emphysema, and often had to direct wearing an oxygen mask. "I think Pauline Kael said about that film, it was easier for him to direct than breathe," says Anjelica. "Because I was so sad to see him so sick, I was depressed, too. But he was amazing, completely in charge. It went as smooth as glass."

In John's absence, Anjelica is now the de facto head of the Huston dynasty. The longevity of her own career would make Hepburn proud, and she's now been adopted by a new generation of film-makers, including Wes Anderson. Younger brother Danny is a regular Hollywood fixture, currently in Ridley Scott's Robin Hood, and there are fourth-generation Hustons coming on to the scene, too, such as her nephew Jack, who's in the next Twilight movie.

"There's a whole batch coming up," says Anjelica. "I think of them as colts and fillies in the back stable. The family bonds spread ever wider and they tie ever tighter. Once we cleave together, that's it."

Anjelica Huston and Angela Allen will be in conversation at a screening of the restored African Queen at the BFI, London (020-7928 3232), on 27 May. The DVD is out on 14 June.